Topic and tone of political news articles in German online media.
Franziska Löw
April 2018
I conduct a STM (Strucutral Topic Model) estimation on a sample of 14,936 online news articles from seven news provider about domestic politics: Bild.de, DIE WELT, FOCUS ONLINE, SPIEGEL ONLINE, Stern.de, ZEIT ONLINE, Tagesschau.de. The articles are dated from 01.06.2017 to 01.03.2018 (German federal elections took place on 24th of September 2017.). I first extract all online articles using the the Eventregistry API. Then all articles from the section “domestic policy” are filtered by checking the URL structure. The data cleaning process is documented here.
To discover the latent topics in the corpus, the structural topic modeling (STM) developed by Roberts (2016) is applied. The STM is an unsupervised machine learning approach that models topics as multinomial distributions of words and documents as multinomial distributions of topics, allowing to incorporate external variables that effect both, topical content and topical prevalence. I will included the news provider as a control for both the topical content and the topical prevalence. The number of topics is set to 50.
Data Exploratory Analysis
Distribution of articles
The Figures below show the distribution of the number of articles from the respective news sources by date. There is a high peak around the federal elections on September, 24th and another one shortly after the failure of the Jamaica coalition talks on November, 19th (indicated by the red dotted lines). The Figure on the right shows, that DIE WELT published most articles on domestic policy, followed by stern.de and FOCUS ONLINE.
ggsave({
btw %>%
ggplot(aes(site)) +
geom_bar(fill=col[3], alpha = 0.8) +
labs(x="", y="Number of articles") +
coord_flip() +
theme(
axis.text.y = element_text(size = 12),
legend.position = "none"
)
},
filename = "../figs/bar.png", device = "png",
width = 6, height = 4,
dpi = 600)
plot1
ggsave({
btw %>%
group_by(date) %>%
dplyr::summarise(obs = n()) %>%
ggplot(aes(date, obs)) +
geom_line(color=col[3]) +
geom_vline(aes(xintercept=as.Date("2017-09-24")),
linetype = 2, color=col[5]) +
geom_vline(aes(xintercept=as.Date("2017-11-19")),
linetype = 2, color=col[5]) +
scale_color_manual(values = col) +
labs(x="", y="Number of Articles",color="") +
scale_x_date(breaks = date_breaks("1 month"), labels=date_format("%b\n%y", tz="CET")) +
theme(
legend.position = "none",
axis.title.x = element_blank(),
axis.text = element_text(size = 10)
)
},
filename = "../figs/timeline.png", device = "png",width = 6, height = 4,
dpi = 600
)
plot1
Word Count
Most of the articles have a word length between 200 and 1000 words (articles with less than 200 words were filtered out in advance, as these are mostly reader comments). The distribution at Bild.de, DIE WELT, FOCUS ONLINE and stern.de is left-skewed, whereby stern.de has comparatively many articles with a word length of over 2000.
The longest article at Tagesschau.de has 2006 words, nevertheless the median value is comparatively large (see the Table below). ZEIT ONLINE has the highest median value of 459 words.
output <- describeBy(btw$text_length, btw$site, mat=T)%>%
select(group1, n, mean, sd, median, min, max, se)
rownames(output) <- c()
print(xtable(output, type="latex", caption = "Summary statistics of text length",
ref = "t_wordcount"),
file="../writing/tables/wordcount.tex" )
describeBy(btw$text_length, btw$site)##
## Descriptive statistics by group
## group: Bild.de
## vars n mean sd median trimmed mad min max range skew
## X1 1 1277 475.2 319.22 394 431.5 253.52 121 3710 3589 2.48
## kurtosis se
## X1 13.77 8.93
## --------------------------------------------------------
## group: DIE WELT
## vars n mean sd median trimmed mad min max range skew
## X1 1 3179 507.88 614.28 377 432.34 257.97 121 14507 14386 13.11
## kurtosis se
## X1 248.56 10.89
## --------------------------------------------------------
## group: FOCUS ONLINE
## vars n mean sd median trimmed mad min max range skew
## X1 1 2660 402.68 330.86 299 345.64 185.32 121 5647 5526 4.34
## kurtosis se
## X1 40.74 6.42
## --------------------------------------------------------
## group: SPIEGEL ONLINE
## vars n mean sd median trimmed mad min max range skew
## X1 1 1817 498.96 333.23 387 456.2 253.52 121 3304 3183 2
## kurtosis se
## X1 7.95 7.82
## --------------------------------------------------------
## group: stern.de
## vars n mean sd median trimmed mad min max range skew
## X1 1 2922 518.09 622.99 376.5 409.87 223.13 121 9287 9166 6.51
## kurtosis se
## X1 59.72 11.53
## --------------------------------------------------------
## group: Tagesschau.de
## vars n mean sd median trimmed mad min max range skew
## X1 1 1644 450.34 242.93 397.5 422.13 215.72 121 2006 1885 1.41
## kurtosis se
## X1 3.45 5.99
## --------------------------------------------------------
## group: ZEIT ONLINE
## vars n mean sd median trimmed mad min max range skew
## X1 1 1437 510.98 377.85 459 470.17 217.94 121 8015 7894 9.38
## kurtosis se
## X1 149.73 9.97btw$text_length.cut <- cut(btw$text_length, c(seq(0,2000,1), Inf))
btw <- btw %>% group_by(site) %>%
mutate(text_length.mean = mean(text_length)) %>%
ungroup()
ggsave(plot = {
btw %>%
ggplot(aes(as.numeric(text_length.cut), site)) +
geom_density_ridges(scale = 4,
fill = col[3], alpha = .8,
color = "white") +
labs(x = "Word count", y = "") +
scale_x_continuous(expand = c(0,0),
breaks = c(seq(0,2000,200)),
labels = c(seq(0,1800,200), ">2000")) +
theme(axis.text = element_text(size = 12))
}, filename = "../figs/wordcount.png", width = 8, height = 4)## Picking joint bandwidth of 51.2
Word Count
Wordclouds
To summarise the content of the texts, wordclouds help to get a first impression, as they represent the number of words in a corpus. Intuitively the term frequency (tf) of a word is a measure of how important that word may be. The following word cloud is derived from the whole corpus. As can be seen, problems arise with high frequency words. For example “die”, “der”, and “in” are extremely common but unrelated to the quantity of interest. These terms, often called “stop words”, are important to the grammatical structure of a text, but typically don’t add any additional meaning and can therefore be neglected. We use a pre-defined stop word list from the Snowball stemmer project together with a customized list of stop-words that are redundant or distorting. We also remove punctuation character (e.g. ., ,, !, ?, etc.) and all numbers from our corpus.
Unprocessed Text
Wordcloud
Processed Text
After completing this steps we were left with 68.576 unique terms in our vocabulary. The following wordclouds are derived from the corpus for each news provider. It becomes evident that these are texts discussing domestic policy issues. The SPD in particular seems to be higly frequent. However, at first glance, there are no obvious differences between the corpus of the different news provider.
Model Results
1. Topic
1.1. Label topics
In order to improve readability and traceability, I assign a shorter name to the topics based on the most common words. The plotQuote function allows to inspect die most common words of a topic for each covariate.
topic <- 2
plotQuote(c(paste(sagelabs$covnames[1],":",
paste(sagelabs$cov.betas[[1]]$problabels[topic,], collapse="\n")),
paste(sagelabs$covnames[2],":",
paste(sagelabs$cov.betas[[2]]$problabels[topic,], collapse="\n")),
paste(sagelabs$covnames[3],":",
paste(sagelabs$cov.betas[[3]]$problabels[topic,], collapse="\n")),
paste(sagelabs$covnames[4],":",
paste(sagelabs$cov.betas[[4]]$problabels[topic,], collapse="\n")),
paste(sagelabs$covnames[5],":",
paste(sagelabs$cov.betas[[5]]$problabels[topic,], collapse="\n")),
paste(sagelabs$covnames[6],":",
paste(sagelabs$cov.betas[[6]]$problabels[topic,], collapse="\n")),
paste(sagelabs$covnames[7],":",
paste(sagelabs$cov.betas[[7]]$problabels[topic,], collapse="\n"))),
text.cex = 0.8, width = 40
)topics <- matrix(c(1, "SPD, M.Schulz", 2, "B90/ Die Grünen", 3, "Mix: Akhanli, Guttenberg, Bayern", 4, "Great Coalition debates", 5, "Diesel scandal", 6, "H.Kohl", 7, "Federal Election results", 8, "Europa, Macron, Schäuble", 9, "Mix: political trends, twitter", 10, "M.Schulz, vs. A.Merkel", 11, "politics & democracy in GER", 12, "Deportation of criminal Refugees", 13, "A.Merkel, election campaign", 14, "Text processing fail", 15, "Israel, antisemitism, D.Trump", 16, "Mix: political talkshows, Refugees", 17, "Debates within SPD", 18, "Election in Niedersachsen", 19, "N.Lammert", 20, "AfD, right-wing radicalism", 21, "German armed forces, v.d.Leyen", 22, "SPD, stuffing debates", 23, "CSU, Söder & Seehover", 24, "Bundespräsident F.-W.Steinmeier", 25, "Election polls", 26, "Jamaica fail, Reelections or GroKo?", 27, "Jamaica Coalition debates", 28, "G20 in Hamburg", 29, "Federal Constitutional Court, Ministry of the Interior", 30, "AfD, F.Petry & Meuthen", 31, "D.Trump, Russia", 32, "AfD, Gauland & Weidel", 33, "German armed forces, Mali", 34, "Mix: Children, Education, Women", 35, "Left- rightwing Terror, police reports", 36, "Mix: people, Germany, democracy", 37, "AfD & DIE LINKE in parliament", 38, "EU policies", 39, "Mix: Terror attacks", 40, "Mix: Metoo, SPD", 41, "Terror attack Berlin (Amri)", 42, "Refugee family reunion", 43, "Mix: studies", 44, "Federal Constitutional Court (NSU, Franco, Terror)", 45, "Mix: minister of the interior, environment", 46, "CDU", 47, "Church", 48, "public (budget) statistics, Education/ Healthcare/ Digital policies", 49, "Turkey", 50, "Höcke, Holocaust"), ncol=2, byrow=T)
topics.df <- as.data.frame(topics) %>%
transmute(topic_name = paste(V1, V2, sep=": "),
topic = 1:k) 1.2. Posterior distribution (gamma)
The theta Matrix is a DxK Matrix that gives us a probability for each topic (K) and each document (D)
# Document-topic probabilities
stmOut %>% tidy("theta") -> thetaTo get a better understanding of the distribution of the “highest gamma”, we assign a topic to each document (topic with highest postertior distribution).
top_topics <- theta %>%
group_by(document) %>%
mutate(therank = rank(-gamma)) %>%
filter(therank == 1) %>%
select(- therank)
btw.2 <- btw %>%
mutate(document = articleID) %>%
merge(.,top_topics, by="document") %>%
## Combine with Topic label
merge(., topics.df, by="topic") %>%
mutate(allocation = 1) ggplot(btw.2, aes(gamma)) +
geom_density(fill=col[3], alpha = 0.8,
color = col[3]) +
labs(title = "Density Plot / Posterior distribution",
y = "Theta")
1.3 Topic proportions
In order to get an initial overview of the results, the figure below displays the topics ordered by their expected frequency across the corpus. To assign a label to each topic, I looked at the most frequent words in that topic and the most representative articles.
keep <- seq(1:k)Here, I create a Dataframe that contains the columns means of theta (per topic and covariate level)
frequency <- as.data.frame(colMeans(stmOut$theta)) %>%
mutate(frequency = colMeans(stmOut$theta),
topic = topics[,1],
topic_name=paste(topics[,1],topics[,2],
sep=": ")) %>%
filter(topic %in% keep)
freq <- tapply(stmOut$theta[,1], stmOut$settings$covariates$betaindex, mean)
freq <- as.data.frame(freq) %>%
mutate(site=stmOut$settings$covariates$yvarlevels,
topic = 1)
for(i in 2:k) {
freq1 <- tapply(stmOut$theta[,i], stmOut$settings$covariates$betaindex, mean)
freq1 <- as.data.frame(freq1) %>%
transmute(site=stmOut$settings$covariates$yvarlevels,
topic = i,
freq = freq1)
freq <- rbind(freq, freq1)
}
freq <- freq %>%
left_join(., topics.df, by = "topic") %>%
#filter(topic %in% keep) %>%
mutate(topic = topic_name) %>%
left_join(., frequency %>% select(topic, frequency),
by = "topic")Next, we can plot the expected proportion of topic use in the overall corpus vs. the expected proportion of topic use for each medium.
Topic Proportion
Topic Proportion
We will conduct our further analysis on 15 selected topics which relate to political parties.
keep <- c(1,2,4,10,13,17,20,22,23,26,27,30,32,37,46)1.4. Difference in topic prevalence
To identify which of these differences is significant, the conditional expectation of topic prevalence for given document characteristics can be estimated. More specifically, I estimate a linear model, where the documents are observations, the dependent variable is the posterior probability of a topic and the covariates are the metadata of documents.
The estimateEffect() uses the method of composition to incorporate uncertainty in the dependent variable, drawing a set of topic proportions from the variational posterior repeated times and compute the coefficients as the average over all results.
effect <- estimateEffect(c(1:k) ~site, stmOut,
metadata = out$meta, uncertainty = "None")Here, I create a dataframe that contains the results of the estimation.
tables <- vector(mode="list", length = length(effect$topics))
for (i in seq_along(effect$topics)) {
sims <- lapply(effect$parameters[[i]], function(x) stm:::rmvnorm(500, x$est, x$vcov))
sims <- do.call(rbind, sims)
est <- colMeans(sims)
se <- sqrt(apply(sims,2, stats::var))
tval <- est/se
rdf <- nrow(effect$data) - length(est)
p <- 2*stats::pt(abs(tval), rdf, lower.tail = FALSE)
topic <- i
coefficients <- cbind(topic, est, se, tval, p)
rownames(coefficients) <- attr(effect$parameters[[1]][[1]]$est, "names")
colnames(coefficients) <- c("topic", "Estimate", "Std. Error", "t value", "p")
tables[[i]] <- coefficients
}
out1 <- list(call=effect$call, topics=effect$topics, tables=tables)
coeff <- as.data.frame(do.call(rbind,out1$tables))
coeff <- coeff %>%
mutate(parameter = rownames(coeff),
parameter = gsub("site", "", parameter),
signifcant = ifelse(p <= 0.5,"yes","no")) %>%
left_join(., topics.df, by="topic") %>%
mutate(parameter = ifelse(parameter == "welt.de", "DIE WELT", parameter),
parameter = ifelse(parameter == "zeit.de", "ZEIT ONLINE", parameter),
parameter = ifelse(parameter == "focus.de", "FOCUS ONLINE", parameter),
parameter = ifelse(parameter == "spiegel.de", "SPIEGEL ONLINE", parameter),
parameter = ifelse(parameter == "tagesschau.de", "Tagesschau.de", parameter))The following figure shows the regression results for each news page. The coefficients indicate the deviation from the base value of Bild.de (keeping the month equal).
p1 <- coeff %>%
filter(topic %in% keep) %>%
filter(parameter != "(Intercept)") %>%
ggplot(aes(x = reorder(topic_name,topic, decreasing=F), y = Estimate, fill=factor(signifcant))) +
geom_col(alpha = 0.8) +
scale_fill_manual(values = col[c(5,3)]) +
scale_x_discrete(position = "top") +
geom_hline(yintercept = 0, linetype = 2,
color = "black") +
coord_flip() +
facet_wrap(~parameter, ncol = 8, scales = "free_x") +
labs(x="", fill="significant at the 5% level") +
theme(legend.position = "top",
axis.text.y = element_text(size=11),
axis.text.x = element_text(angle=90))
ggsave(plot = p1, filename = "../figs/estimates.png", device = "png",width = 9, height = 6,
dpi = 600)
Estimates
2. Tone
2.1. Plotquote
The plotQuote function allows to inspect die most common words of a topic for each covariate.
2.2. Sentiment analysis
keep <- c(1,2,4,10,13,17,20,22,23,26,27,30,32,37,46)The idea of Sentiment analysis is to determine the attitude of a writer through online text data toward certain topic or the overall tonality of a document.
Lexical or “bag-ofwords” approaches are commonly used. In that approach, the researcher provides pre-defined dictionaries (lists) of words associated with a given emotion, such as negativity. The target text is then deconstructed into individual words (or tokens) and the frequencies of words contained in a given dictionary are then calculated.
2.2.1. Load sentiment dictionary.
SentimentWortschatz, or SentiWS for short, is a publicly available German-language resource for sentiment analysis, opinion mining etc. It lists positive and negative polarity bearing words weighted within the interval of [-1; 1] plus their part of speech tag, and if applicable, their inflections. The current version of SentiWS (v1.8b) contains 1,650 positive and 1,818 negative words, which sum up to 15,649 positive and 15,632 negative word forms incl. their inflections, respectively. It not only contains adjectives and adverbs explicitly expressing a sentiment, but also nouns and verbs implicitly containing one.
sent <- c(
# positive Wörter
readLines("dict/SentiWS_v1.8c_Negative.txt",
encoding = "UTF-8"),
# negative Wörter
readLines("dict/SentiWS_v1.8c_Positive.txt",
encoding = "UTF-8")
) %>% lapply(function(x) {
# Extrahieren der einzelnen Spalten
res <- strsplit(x, "\t", fixed = TRUE)[[1]]
return(data.frame(words = res[1], value = res[2],
stringsAsFactors = FALSE))
}) %>%
bind_rows %>%
mutate(word = gsub("\\|.*", "", words) %>% tolower,
value = as.numeric(value)) %>%
# manche Wörter kommen doppelt vor, hier nehmen wir den mittleren Wert
group_by(word) %>% summarise(value = mean(value)) %>% ungroupsamp <- sent %>% dplyr::sample_n(10)
print(xtable(samp, type="latex", label = "t_sentdict",
caption = "Sentiment Dictionary (Sample)"),
file="../writing/tables/sent_dict.tex" )
knitr::kable(samp)| word | value |
|---|---|
| brisant | -0.0048 |
| makel | -0.1813 |
| vergöttern | 0.0040 |
| gediegen | 0.0831 |
| mühe | -0.0048 |
| untreue | -0.3293 |
| unhöflich | -0.0048 |
| erschweren | -0.4891 |
| addieren | 0.0040 |
| fehlleistung | -0.0048 |
2.2.2. Apply the dictionary on the artciles.
To carry out the sentiment analysis we filter some documents from the corpus:
- Articles that have been assigned a topic with a probability of over 30% (gamma > 0.3).
- Articles assigned to one of the above mentioned topics.
- Some manual cleanups
After applying these filters, we still have about 2500 articles left to conduct the sentiment analysis. We now take each word in each article and assign a sentiment value for that word.
2.2.3. Check the analysis for a set of example documents.
2.2.4. Calculate sentiment value by document
The sentiment score is calculated based on the weighted polarity values for a word, defined on an interval between -1 and 1. The score is then calculated from the sum of the words in a document (which can be assigned to a word from the dictionary) divided by the total number of words in that document.
\[ \text{SentScore}_d = \frac{|\text{positive polarity score}_d| - |\text{negative polarity score}_d|}{\text{Total Words}_d} \]
sentDF.values <- sentDF %>%
select(document, word, value,
negative, positive,
negative_d, positive_d) %>%
group_by(document) %>%
# calculate sum of positive and negative values
summarise(sum_positive = sum(positive, na.rm = T),
sum_negative = sum(negative, na.rm = T),
sum_positive_d = sum(positive_d, na.rm = T),
sum_negative_d = sum(negative_d, na.rm = T)) %>%
# calculate diff
mutate(sent_diff = sum_positive + sum_negative,
sent_diff_d = sum_positive_d - sum_negative_d) %>%
# combine with dataframe
left_join(., df,
by = "document") %>%
# calculate sentiment
mutate(sentiment_d = sent_diff_d / text_length,
sentiment = sent_diff / text_length) %>%
# generate month & week
mutate(week = week(date),
month = month(date),
year = year(date),
yearmonth = calculate_month(month,year),
yearweek = calculate_week(week, year)) 2.2.5. Plot Sentiment Score
btw.2 %>%
mutate(yearmonth = calculate_month(month(date), year(date))) %>%
group_by(yearmonth) %>%
summarise(total_obs = n()) -> tally_month
btw.2 %>%
group_by(site) %>%
summarise(total_obs = n()) -> tally_site
btw.2 %>%
mutate(yearmonth = calculate_month(month(date),year(date))) %>%
group_by(yearmonth, site) %>%
summarise(total_obs = n()) -> tally_month_siteThe following table shows the results of the analysis for each topic on a monthly basis, aggregated on all newspaper. Each sentiment value is weighted by the relative share of the topic in the overall reporting of that month.
\[ \text{w} = \frac{\text{# of documents per month & topic}}{\text{# of documents per month}} \]
\[ \text{weighted sentiment} = \text{sentiment} * \text{w} \]
Some conclusions can be drawn from this illustration. First of all, it can be seen that, on average, all topics are discussed almost exclusively negatively. An exception is topic 27 concerning the Jaimiaca coalition negotiations, which shows a positive sentiment value for a short period of time (October 2017). In the following month (November 2017), after it became clear that there would be no coalition between the CDU/CSU, FDP and Die Grünen, the value of this topic as well as that of topic 26 drops rapidly.
Concerning the issues that discuss the great coaltion between CDU/CSU and SPD, it is evident that the overall tone is in which this topic is discussed is generally decreasing from November 2017 to January 2018, but in the following February, the sentiment value of this topic rises. However, the sentiment score of topics that deal with the SPD alone (1, 17, 22) is diminishing in the course of time, with topic 17 recording the largest decline. The topic, which contains the CDU in isolation (46), is rather zigzagging, with a low peak in October 2017.
By Month & Topic
p %>%
knitr::kable()| x |
|---|
| 0.3282815 |
| 0.0541077 |
| 0.6864584 |
| 0.0189246 |
| 0.8458273 |
| 0.1142537 |
| 0.9577611 |
\[ \text{normalized_w} = \frac{w - \min{(W)}}{\max{(W)}-\min{(W)}} \]
Monthly Sentiment Score
By Site and Topic
The following figure shows the results of the analysis for each topic and each newspaper, aggregated over time. Each sentiment value is weighted by the relative share of the topic in the overall political news coverage of that online newspaper.
\[ \text{w} = \frac{\text{# of obs per newspaper & topic}}{\text{# of obs per newspaper}} \]
\[ \text{weighted sentiment} = \text{sentiment} * \text{w} \]
p %>%
knitr::kable()| x |
|---|
| 0.3282815 |
| 0.0541077 |
| 0.6864584 |
| 0.0189246 |
| 0.8458273 |
| 0.1142537 |
| 0.9577611 |
Sentiment Score by Newssite
Radar plot
require(ggiraph)
require(ggiraphExtra)
Radarplot Sentiment Score
3. Compare with polls
We use the data from the “Sonntagsumfrage” (Sunday survey) from infratest dimap. The institution regularly asks at least 1000 German citizens the question: “Which party would you choose if federal elections take place next Sunday?” The survey thus measures the current election tendencies and therefore reflects an intermediate state in the opinion-forming process of the electoral population.
# Import and prepare survey data
load("../output/polls.Rda")
polls <- table_long %>%
mutate(yearmonth = calculate_month(month(Datum),year(Datum)),
yearweek = calculate_week(week(Datum), year(Datum))) 
###### Normalization The comparison with the sentiment value of individual topics is intended to show whether there is a correlation between the current tendency to vote and the type of reporting. For this purpose, the monthly average of both time series is calculated and rescaled to an interval between 0 and 1.
The analysis in this section is done in two steps: First, the standardised time series are compared graphically. In the second step, the cross-correlation between two time series is calculated.
\[ z_i = \frac{x_i-\text{min}(x)}{\text{max}(x)-\text{min}(x)} \] where \(x = (x_1,...,x_n)\) and \(z_i\) is the \(i^{th}\) normalized data.
polls_monthly <- polls %>%
group_by(yearmonth,party) %>%
summarise(mean_val = mean(value, na.rm=T)) %>%
ungroup() %>%
filter(!party %in% c("Piraten", "Sonstige")) %>%
filter(mean_val != "NaN") %>%
select(party, yearmonth, mean_val) %>%
spread(party, mean_val) %>%
filter(yearmonth > as.Date("2017-05-01")) %>%
filter(yearmonth < as.Date("2018-03-01")) %>%
mutate(AfD = normalize_data(AfD),
FDP = normalize_data(FDP),
Grüne = normalize_data(Grüne),
Linke = normalize_data(Linke),
SPD = normalize_data(SPD),
Union = normalize_data(Union))Normalize topic-sentiment value
### by time
group1 <- sentDF.values %>%
group_by(yearmonth, topic_name, topic) %>%
summarise(sentiment = mean(sentiment, na.rm=T),
obs = n()) %>%
ungroup() %>%
left_join(., tally_month, by="yearmonth") %>%
mutate(w = obs / total_obs,
sentiment_w = sentiment * w)
group1 <- group1 %>%
select(yearmonth, topic, sentiment_w) %>%
spread(topic, sentiment_w) %>%
lapply(normalize_data) %>%
as.data.frame() %>%
gather(topic, sentiment_n, -yearmonth) %>%
mutate(topic = as.numeric(gsub("X","", topic))) %>%
merge(., group1, by = c("topic", "yearmonth"))
### by time and site
group2 <- sentDF.values %>%
group_by(yearmonth, topic_name, topic, site) %>%
summarise(sentiment = mean(sentiment, na.rm=T),
obs = n()) %>%
ungroup() %>%
left_join(., tally_month_site, by=c("yearmonth","site")) %>%
mutate(w = obs / total_obs,
sentiment_w = sentiment * w)
group2 <- group2 %>%
select(yearmonth, topic, site, sentiment_w) %>%
spread(topic, sentiment_w) %>%
lapply(normalize_data) %>%
as.data.frame() %>%
gather(topic, sentiment_n, -yearmonth, -site) %>%
mutate(topic = as.numeric(gsub("X","", topic))) %>%
merge(., group2, by = c("topic", "yearmonth","site"))3.1. Cross-Correlation
3.1.1. Overall
group1 %>%
select(yearmonth, topic_name, sentiment_n) %>%
spread(topic_name, sentiment_n) %>%
select(- yearmonth) -> corr1
polls_monthly %>% select(- yearmonth) -> corr2# Create empty matrix
corr <- expand.grid(names(corr1), names(corr2))
corr$`-3` <- NA
corr$`-2` <- NA
corr$`-1` <- NA
corr$`0` <- NA
corr$`1` <- NA
corr$`2` <- NA
corr$`3` <- NA
x <- 1
for (corr1Id in 1:ncol(corr2)) {
c1 = corr2[,corr1Id]
for(corr2Id in 1:ncol(corr1)) {
c2 = corr1[,corr2Id]
correlation = ccf(c2, c1, lag.max = 3,
na.action = na.contiguous, plot=F)
corr[x,"-3"] <- correlation$acf[1]
corr[x,"-2"] <- correlation$acf[2]
corr[x,"-1"] <- correlation$acf[3]
corr[x,"0"] <- correlation$acf[4]
corr[x,"1"] <- correlation$acf[5]
corr[x,"2"] <- correlation$acf[6]
corr[x,"3"] <- correlation$acf[7]
x<- x+1
}
}
corr <- corr %>%
gather(lag, correlation, `-3`:`3`) %>%
mutate(lag = as.numeric(lag))The variance of the cross-correlation coefficient under the null hypothesis of zero correlation is approx \(1/n\) where \(n\) is the length of the series. The coefficients are also asymptotically normal. So approximate critical values (at the 5% level) are \(\pm 2/\sqrt{n}\).
critical_val <- 2/sqrt(nrow(corr1))p <- ggplot(corr, aes(lag, correlation,
#fill = Var1,
group=Var2)) +
geom_col(fill = col[3]) +
#scale_x_continuous(breaks = c(-3:3)) +
labs(x="Lag",y="Cross Correlation",
caption = "The red dotted lines indicate the critical values at the 5% significance value\nThe black dotted lines indicate the lag 0 on the x-axis.") +
geom_hline(yintercept = critical_val, linetype = 2, color = col[5]) +
geom_hline(yintercept = -(critical_val), linetype = 2, color = col[5]) +
geom_vline(xintercept = 0, linetype = 3, size=0.5) +
facet_grid(Var2~Var1, labeller=labeller(Var1 = linebreak)) +
theme(strip.text = element_text(size=13),
axis.text = element_text(size = 12),
axis.title = element_text(size=14),
plot.caption = element_text(size = 10, hjust = 0))
ggsave(filename = "../figs/ccf2.png", plot = p,
width = 18,
height = 12,
dpi = 600)
Cross-correlation 2
Cross correlation at lag 0
# Table
corr %>%
filter(lag == 0) %>%
select(-lag) %>%
spread(Var2, correlation) -> corr_tab
print(xtable(corr_tab, type="latex", digits=3,
label = "t_ccf",
caption = "Cross Correlation at lag 0"),
file="../writing/tables/corr.tex" )# Figure
p <- corr %>%
filter(lag == 0) %>%
ggplot(aes(Var2, Var1,
fill = correlation,
label = round(correlation,2))) +
geom_tile(color="white", alpha=0.8) +
geom_text(size = 3.5) +
#viridis::scale_fill_viridis(limits=c(-1, 1)) +
labs(x="", y="", fill="",
title = "",
subtitle = "Election polls vs. topic sentiment value (monthly)")
ggsave(filename = "../figs/ccf.png", plot = p,
height = 6, width = 8, dpi = 600)
Cross-correlation